A flip in an array A[1:n] of numbers is a pair of indices (i, j) such that i < j and A[i] > A[j]. In other words, a flip is a pair of elements that are not in sorted order. By modifying merge sort, design an algorithm that counts the number of flips in an array of length n in O(n log n) time. (Note: There can be (n^2) flips in an n-element array, so your algorithm cannot explicitly list them and achieve the time bound. It is possible to count flips without listing them.)